Photo-induced semimetallic states realised in electron–hole coupled insulators

Using light to manipulate materials into desired states is one of the goals in condensed matter physics, since light control can provide ultrafast and environmentally friendly photonics devices. However, it is generally difficult to realise a photo-induced phase which is not merely a higher entropy phase corresponding to a high-temperature phase at equilibrium. Here, we report realisation of photo-induced insulator-to-metal transitions in Ta2Ni(Se1−xSx)5 including the excitonic insulator phase using time- and angle-resolved photoemission spectroscopy. From the dynamic properties of the system, we determine that screening of excitonic correlations plays a key role in the timescale of the transition to the metallic phase, which supports the existence of an excitonic insulator phase at equilibrium. The non-equilibrium metallic state observed unexpectedly in the direct-gap excitonic insulator opens up a new avenue to optical band engineering in electron–hole coupled systems.


Introduction.
In semimetals or small-gap semiconductors, valence-band holes and conduction-band electrons may form bound states or excitons via weakly screened Coulomb interaction.
The excitons condensate in a Bardeen-Cooper-Schrieffer (BCS) or Bose-Einstein condensation (BEC) manner, depending on whether the electron-hole coupling is weak or strong, and such a ground state is theoretically predicted as an excitonic insulator 1 .
One of the prototypical candidates of excitonic insulators is 1T-TiSe2, which shows a charge-density-wave (CDW) transition accompanying a 2×2×2 structural distortion at ~ 202 K 2,3 . Figure 1a illustrates a canonical phase diagram of excitonic insulators, and 1T-TiSe2 indeed exhibits such a phase diagram. One of the most plausible evidence that 1T-TiSe2 is an excitonic insulator has been reported by Hellmann et al 4

. They have classified several CDW insulators by their dominant interactions to Mott, excitonic, and
Peierls insulators based on their melting times of electronic order parameters by timeand angle-resolved photoemission spectroscopy. In addition, a recent electron energy loss spectroscopy study on 1T-TiSe2 has reported an electronic collective mode coupled to phonons expected for an excitonic insulator 5 . However, since 1T-TiSe2 has indirecttype electron and hole bands (the valence band maximum and the conduction band 3 minimum are located at different positions in the Brillouin zone), and its excitonic condensation is inevitably accompanied by a band folding with a finite wave vector q like a Peierls insulator, it is still difficult to exclude contribution of electron lattice interaction. Also the indirect gap is not favourable for optical control of electrons and holes for future application.
On the other hand, Ta2NiSe5, which has been supposed to be a unique candidate of excitonic insulators in the strong coupling (BEC) regime, has a quasi-one-dimensional structure composed of layers of Ni single chains and Ta double chains along the a-axis ( Fig. 1b), and each layer is stacked by van der Waals interactions 6,7 . Hybridised Ni 3d and Se 4p orbitals mainly compose the valence band near the Fermi level (EF), whereas Ta 5d orbitals primarily form the doubly degenerate conduction bands (Fig. 1c) 6,7 . This degeneracy can be partially lifted by the finite hybridisation between the two Ta chains.
When the temperature decreases, Ta2NiSe5 undergoes a semiconductor-to-insulator transition at 328 K, accompanied by a structural distortion from orthorhombic to monoclinic symmetry 6,7,8 . According to the angle-resolved photoemission spectroscopy (ARPES) measurements in the equilibrium state, it has been found that the top portion of the valence band remarkably becomes flat below the transition temperature. This has been considered as evidence for the spontaneous formation of excitons between the Ta 5d electron bands and the Ni 3d-Se 4p hybridised hole bands and thus, a phase transition to an excitonic insulator in the strong coupling regime [9][10][11][12] . Recently, Lu et al., have established the phase diagram of Ta2Ni(Se1-xSx)5 which covers the excitonic insulator phase and the band insulator phase as a function of x 13 . However, more direct evidence for the excitonic insulating phase is still lacking so far. If the similar behaviour of the pump-fluence dependence to the photo-excitation to 1T-TiSe2 is observed also in Ta2NiSe5, it will strengthen that the behaviour can be regarded as the evidence for the excitonic insulating phase. 4 For the present study, we have performed the measurements of time-and angleresolved photoemission spectroscopy (TARPES) to obtain such evidence that Ta2NiSe5 is actually an excitonic insulator from its pump-fluence dependence of the photoexcitation dynamics. Whereas several time-resolved studies on Ta2NiSe5 have been reported so far [14][15][16][17] , the present study is quite unique in that we employ a pump laser with shorter pulse duration (~ 30 fs), and extreme ultra violet (XUV) laser from high harmonic generation for probe pulses. Whereas we have employed 1 kHz for the repetition rate of the laser in order to generate higher order harmonics, this makes higher pump fluence available compared to higher repetition rate with the same average power of pump pulses. This would be the reason why we obtained the rather different TARPES results from Mor et al., which have revealed the band gap narrowing and the enhanced excitonic coupling in Ta2NiSe5 by photo-excitation 15 . We do observe that slightly S-substituted Ta2NiSe5 shows a characteristic pump-fluence dependence in its excitation dynamics, whereas Ta2NiS5, which had been considered as an ordinary band insulator, shows no dependence. Furthermore, quite unexpectedly, we find a nonequilibrium metallic phase as a photo-excited state of slightly S-substituted Ta2NiSe5 as well as Ta2NiS5. Whereas our results strongly suggest that Ta2NiSe5 is an excitonic insulator, our observation of non-equilibrium metallic phase in both of slightly Ssubstituted Ta2NiSe5 and Ta2NiS5 may require reconsidering that Ta2NiS5 is not an ordinary band insulator. We propose the importance of the electron correlation effect for the insulating ground state of Ta2NiS5. In addition, our findings serve a new pathway to phase control of materials including excitonic insulators by light.

Pump-fluence dependence
First, we demonstrate that Ta2NiSe5 (hereafter, 3% S-substituted Ta2NiSe5 used in this study is simply referred as Ta2NiSe5, since the electronic structure is almost not 5 affected by the substitution as shown in Supplementary Fig. 2) shows a characteristic pump-fluence dependence to photo-excitation similar to another candidate of excitonic insulators, 1T-TiSe2. Figure 2a shows an energy-momentum (E-k) map around the  point (centre of the Brillouin zone) taken before the arrival of the pump pulse at 100 K.
The overall features of the spectra are confirmed to be consistent with those of the spectrum taken at equilibrium, especially for the gap of ~ 250 meV, and this certifies that distortion of the spectra due to space charge effects, which could often occur for TARPES measurements with a low repetition frequency such as 1 kHz, has been minimized. After the arrival of the pump pulse, the spectral weight of the flat band immediately decreases and is transferred to the originally gapped region at EF within 100 fs. This temporal evolution is shown in Fig. 2b. These dynamics are much faster than excess energy transfer from hot electrons to the cold phonon bath, which has been generally reported to require ~ 1 ps and are more likely to be associated with purely electronic process, which has been supposed to be ~ 100 fs or faster 18, 19 In order to The time scale of the gap collapse in excitonic insulators is considered to be inversely proportional to the plasma frequency, p = (ne 2 /rm*) 1/2 , where n is the carrier density, e is the elementary charge and m* is the effective mass of the valence or conduction band, 0 is the electric constant, and r is the dielectric constant 4,20 . From this 6 relationship, the gap quenching time should be proportional to 1/√n. Since the ground state of Ta2NiSe5 is an insulating phase and the carrier density n in the equilibrium state is expected to be quite small, the carrier density n in the photo-excited state is expected to be nearly proportional to the pump fluence. We found that the drop time flat of Ta2NiSe5 was proportional to 1/F 0.7 , where F is the pump fluence (Fig. 2d). On the other hand, we have performed the similar measurements also on Ta2NiS5 and the results are shown in Supplementary Fig. 3. The drop time of the top portion of the valence band was deduced from the fitting, and is plotted as red symbols in Fig. 2d. Contrastingly, it does not show clear pump fluence dependence. Thus, our results strongly suggest that Ta2NiSe5 is an excitonic insulator, but Ta2NiS5 is not (The behaviour of Ta2NiS5 is discussed later again). At least, the band gap of Ta2NiSe5 appears to originate from an electronic mechanism similar to that of 1T-TiSe2.

Temporal evolution of TARPES spectra
Next, we show more impressive temporal evolution of TARPES spectra of Ta2NiSe5. Figures 3a and 3b show the temporal evolution of the momentum-integrated energy distribution curve (EDC) and its integrated intensity above EF, respectively.
After the arrival of pump pulse, the intensity above EF immediately increases and relaxes with a time constant of 620 fs, which was estimated from the fitting to a Gaussian-broadened exponential decay function. Figures 3c and 3d show TARPES snapshots acquired at several t values and their differential spectra which were obtained by subtracting the spectrum averaged for t < 0, respectively (see also Supplementary Movie 1). The most notable spectral change is the emergence of an electron-like band crossing EF, which is clearly seen in red colour in Fig. 3d at t = 150 and 250 fs. In other words, the system changes from an insulating state into a metallic state by photoexcitation. Figure 3e shows the temporal evolution of the EDCs integrated in the momentum range [−0.1, 0.1] Å -1 . Before the pump pulse arrives, the flat band 7 appears as the strongest peak at E−EF ~ −250 meV. Immediately after pumping (t = 150 fs), the flat band collapses and the spectral weight shifts towards higher energies. At t = 250 fs, the peak intensity of the flat band decreases remarkably compared to the peak at E−EF ~ −640 meV. Meanwhile, the edge at EF was found to follow the Fermi-Dirac distribution, and the electronic temperature was estimated from the fitting to be as high as ~ 720 K. Since the resistivity of Ta2NiSe5 has been reported to become metalliclike above ~ 550 K 7 , the observed metallic bands may correspond to this metallic behaviour at high temperature. However, this high-temperature metallic resistivity originates from thermally excited carriers and the band gap is expected to be finite even at high temperature 13 . Thus, the observed transient metallic phase could be entirely different from that observed at higher temperatures at equilibrium.
To examine the photo-induced metallic phase in more detail, we compare the time-integrated spectra before and after pumping shown in Figs. 4a and 4b, respectively. To confirm that the observed non-equilibrium metallic phase of Ta2NiSe5 can be associated with the excitonic condensation, we have performed comparative TARPES measurements on Ta2NiS5 and the results are shown in Supplementary Fig. 6. Quite 8 unexpectedly, an electron band emerges above EF and the hole band below EF shifts upward. In addition, the bottom of the electron band and the top of the hole band seems to cross EF, and the system seems likely to be semimetallic. This may require reconsidering the nature of the insulating phase for Ta2NiS5, which had been considered as an ordinary band insulator 12 , since the valence state of nickel and tantalum is naively considered as Ni 0+ (3d 10 ) and Ta 5+ (5d 0 ). According to the band-structure calculation based on the density functional theory 21  Actually, the drop time of Ta2NiS5 seems to be faster than the temporal resolution of our TARPES measurements.
However, if the electronic configuration of nickel in Ta2NiS5 is close to d 9 L, this corresponds to that of tantalum close to 5d 1 , and mechanism for the insulating behaviour of Ta 5d electrons must be considered. One possibility is formation of singlet bonds between the localized Ni 3d spins and Ta 5d electrons as well as S 3p holes (a schematic energy diagram is shown in Supplementary Fig. 7). If one considers that Ta 5d electrons in the double chains form singlet states with the localized d 9 L state via hybridization 9 with the S 3p orbitals, the ground state of Ta2NiS5 can be viewed as a valence-bond-like insulating state which is analogous to a Kondo insulating state. As suggested from the time scale of the gap collapse, the Mottness of the Ni 3d electrons increases from Se to S, and consequently, the nature of ground state is changed from the excitonic insulator to the valence-bond insulator 24 .

Discussion
Lastly, we discuss the mechanism of the photo-induced insulator-to-metal transitions realised in Ta2NiSe5 and Ta2NiS5. Whereas the dynamics of the gap collapse is governed by the interactions of the gap origin, the realization of the non-equilibrium metallic phase cannot be understood straightforward, because no high-temperature metallic phase exists at least for Ta2NiS5. Recently, coherent phonon excitations coupled to the electronic Higgs mode has been found by the pump-probe optical measurements with the similar pump fluence to our TARPES measurements for Ta2NiSe5 14 . Also, an interesting relation between the observed coherent phonon excitations and temperature-dependent Raman spectra has been reported by Mor et al. 16 The coherent phonon excitations observed in various systems 25-27 are most likely explained by the displacive excitation of coherent phonons (DECP) mechanism 28 . In this mechanism, the adiabatic energy potential is modified due to photo-excitations and has the minimum with the finite atomic displacements corresponding to the Ag phonon.
The electronic structure could be modulated by these lattice displacements. The  29 and S is a lighter element than Se, and thus, regarded to be comparable to the 10 observed gap collapse. If the observed metallic phase is driven by the modulation of the electronic structure due to the coherent lattice displacements, whereas incoherent lattice displacements driven by a large electronic density redistribution due to the strong pump pulses also could induce such modulation, as schematically shown in Fig. 1a, the observed photo-induced transition cannot correspond to the dashed vertical arrow, but may rather correspond to the solid arrow. At least, as described above, the nonequilibrium metallic phases observed for both of Ta2NiSe5 and Ta2NiS5 should suggest that these photo-induced phase transitions are not merely transitions to higher entropy states that can be realised at high temperatures in the equilibrium state, but correspond to the dashed vertical arrow in Fig. 1a. Thus, photo-excitation can induce similar effects to pressure, and as the pressure-induced superconducting phase has been found for Ta2NiSe5, with some appropriate pumping condition probably with lower photon energy of some resonant condition, which would not give too much electronic entropy to the system, photo-induced superconductivity might be realised for this material. Realisation of this fascinating photo-induced phase would be one of the ultimate goals of investigations of the photo-excited electronic state.

Methods
Sample preparation. High-quality single crystals of Ta2Ni(Se0.97S0.03)5 and Ta2NiS5 were grown by the chemical vapour transport method. Whereas the relatively large cleaved surface is necessary for TARPES measurements compared to static ARPES, since Ta2NiSe5 has a one-dimensional crystal structure, the large cleaved surface of the pristine Ta2NiSe5 enough for TARPES measurements was difficult to obtain. However, sufficiently large cleaved surfaces of 3% S-substituted Ta2NiSe5 and Ta2NiS5 could be obtained. This is why we used 3% S-substituted Ta2NiSe5 rather than the pristine Ta2NiSe5 for this study. The results of resistivity measurements by commercial physical property measurement system (PPMS, Quantum Design) for the sample characterization 11 is shown in Supplementary Fig. 1. The critical temperature of the structural transition of 3% S-substituted Ta2NiSe5 is determined to be ~ 321 K, whereas that of the pristine Ta2NiSe5 is ~ 325 K. Clean surfaces were obtained by cleaving in situ.
Photoemission measurements. In order to characterise the cleaved surfaces and compare with the previous results, temperature-dependent static ARPES measurements were performed with a He discharge lamp and a hemispherical electron analyser (Omicron-Scienta R4000) with the energy resolution of ~12.5 meV. The results were shown in Supplementary Fig. 2. We confirmed that the temperature dependence of the top of the flat band of the 3% S-substituted sample was almost the same as the previously reported one for the pristine samples, and thus that the electronic structure was almost not affected by the 3 % substitution. For the TARPES measurements, an extremely stable commercial Ti:Sapphire regenerative amplifier system (Coherent Astrella) with a centre wavelength of 800 nm (h = 1.55 eV) and pulse duration of ~30 fs was used for the pump light. After generating a second harmonic (SH) via 0.2-mmthick -BaB2O4, the SH light was focused into a static gas cell filled with Ar and high harmonics were generated 30 . We selected the ninth harmonic of the SH (h = 27.9 eV) for the probe light by using a set of SiC/Mg multilayer mirrors 31 . The temporal resolution was evaluated to be ~80 fs from the TARPES intensity far above the Fermi level corresponding to the cross-correlation between pump and probe pulses. The energy resolution of the spectrometer was set to ~250 meV for the TARPES measurements.
Data availability. The data supporting the findings of this study are available from the corresponding author on request.   for the pristine and substituted samples are plotted by grey and red lines, respectively. The inset shows the activation energy (E = -kBT 2 (ln/T)) deduced from the resistivity data.
Compared to the pristine sample, the critical temperature of the substituted sample is lower by ~4 K, but the activation energy is almost the same between these two compositions.